1. Field of the Invention
The present invention relates generally to optics and, in particular, to determining refractive index distribution in optics for microlitography.
2. Description of the Related Art
Improvement in the manufacturing accuracy of optical components requires more accurate techniques for measuring the properties of optical components.
A two-dimensional (2D) radial model of gradient index (GRIN) is a measuring technique that can be used to estimate the inhomogeneity of optical materials, such as glass or crystals. The existing 2D GRIN techniques estimate the inhomogeneity in two directions, defined according to a Cartesian axis system.
A 2D radial model for GRIN measurement is used to obtain approximate refractive index description. The 2D radial model estimates the inhomogeneity of the optical material by assuming that the refractive index can vary only in two directions. It also assumes that inhomogeneity is constant through the optical material, along a third Cartesian direction. These assumptions greatly simplify the method, system, and computational complexity required to determine the refractive index, encompassed in a workable range. But they introduce a relatively wide range of error.
As the requirements regarding optical components become stricter, the need for more precise measurement methods and systems becomes apparent. What is needed is a technique to determine the three-dimensional refractive gradient index for the optical components.
The present invention is directed to a method, system and computer program product for determining a three-dimensional refractive gradient index of an object. The object comprises an optical material. The optical material, such as a blank in lithography processes, can be a piece of glass, quartz, plastic or other transparent material, fabricated roughly by molding or shaped into the desired finished part. The method is carried out with an interferometric refractive index measurement system.
First the object is located, with a normal orientation, in the interferometric refractive index measurement system, along a first axis, between a reference surface and a retro-mirror surface. A second and a third axis are normal to each other and normal to the first axis.
Second, first through forth phase differences are measured between: a reference wavefront and a wavefront reflected from a first surface of the object; a reference wavefront and a wavefront reflected from a second surface of the object through the object itself; reference wavefront and wavefront reflected from the surface of the retro-mirror through the object and a reference wavefront and a wavefront reflected from the surface of the retro-mirror without object.
Based on these measurements, first through forth two-dimensional surface deformations are determined for the reference surface, the first surface and the second surface of the object, respectively. An average two-dimensional inhomogeneity of the object is then determined. In one embodiment of the invention, using Zernike polynomials, a plurality of coefficients of approximation are determined.
Further on, the object is moved through a plurality of rotation and positions by angles about the second and the third axis. Phase differences are measured between the reference wavefront and a wavefront reflected from the surface of the retro-mirror through the object for each one of the rotations. A plurality of three-dimensional coefficients of approximation are then determined based on the already-assessed surface deformations. The procedure concludes with the determination of a plurality of Aij coefficients describing a three-dimensional refractive gradient index distribution in the object.
The above method is applied, but not limited to, determining three-dimensional refractive gradient index of lens blank objects, lens objects, of cylindrical volumes of optical material. In the preferred embodiments of the invention, the optical material is glass or plastic.
The interferometric refractive index measurement system is implemented using one of Fizeau, Michaelson, Twyman-Green, Mach-Zehnder or other known or future known interferometers.
In a preferred embodiment of the present invention the source for generating the reference wave front is a laser source.
The invention further provides a method for selecting a plurality of preferred optical elements used to assemble a composite optical system with predetermined parameters. The method comprises the steps of selecting a first through N groups of optical elements, wherein N has a predetermined value, testing each optical element of first through N groups of optical elements, using the above method for determining a three-dimensional refractive gradient index, determining a plurality of optical characteristics for each tested optical element, and selecting at least one preferred optical element from each of first through N groups of tested optical elements, based on the determined optical characteristics to design or otherwise assemble a composite optical system.
Further features and advantages of the invention, as well as the structure and operation of various embodiments of the invention, are described in detail below with reference to the accompanying drawings. It is noted that the invention is not limited to the specific embodiment described herein. Such embodiments are presented herein for illustrative purposes only. Additional embodiments will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein.